Ultrasonic bone motion tracking system

ABSTRACT

A computerized bone motion tracking system according to one exemplary embodiment is configured to: provide a non-invasive means for accurate measurement and tracking of the motion of a bone using a volumetric ultrasound transducer and a three dimensional position measurement system; provide relative measurements of one bone relative to another bone of a joint; decompose relative joint motion into specific components; and measure joint instability and range of motion.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. patent application Ser. No.60/945,249, filed Jun. 20, 2007, which is hereby incorporated byreference in its entirety.

TECHNICAL FIELD

The present invention relates to the field of computer-assisted surgeryand human movement analysis and in particular, to the non-invasivetracking of bone structures.

BACKGROUND

In the field of computer assisted surgery, it is often required to tracka structure in a human body, such as a bone or an organ. In particular,in computer assisted orthopaedic surgery, the motion of bones is trackedwith a three-dimensional (3D) position measurement system. This istypically carried out by attaching a marker to the bone invasively, bydrilling pins or screws into the bone, creating holes and causing traumato the tissue and structure. This can increase the risk of bonefracture, infection, and cause pain to the patient. Some examples ofthese intra-operative motion tracking systems can are described in U.S.Patent Application publication No. 20060250300 entitled ‘RF system fortracking objects’ and in U.S. Patent Application Publication No.20050245821 entitled “Position Sensing System for OrthopedicApplications”, each of which is hereby incorporated by reference in itsentirety.

Furthermore, such systems are not suitable for measuring the motion of asubject or patient outside of the operating room, when the patient isnot under anesthesia. This is due to the invasiveness of currenttracking systems, and the abovementioned factors. Normally, in theanalysis of human movement, such as in gait analysis, the motion of theunderlying bones is inferred by tracking the motion of the overlyingskin. This is typically carried out by attaching markers to the skinusing adhesive means, or straps, or by attaching markers to fittedclothes on the subject. While not invasive, this method has thedisadvantage of being less accurate, because of the motion of the skinand other overlying soft-tissues such as muscle with respect to the bonesurface.

Other methods for measuring in-vivo bone kinematics use live 2Dprojected fluoroscopy images and intensity-based three-dimensional totwo-dimensional image registration techniques (see for example thearticle by Komistek et. al. entitled In Vivo Fluoroscopic Analysis ofthe Normal Human Knee, in CLINICAL ORTHOPAEDICS AND RELATED RESEARCH,Number 410, pp. 69-81, 2003). Komistek's method requires theconstruction of three-dimensional computer-aided design models frompre-operative segmented computed tomography (CT) or magnetic resonanceimaging (MRI) scans, and to register these models to 2D fluoroscopicimages using an optimization algorithm that automatically adjusts thepose of the model at various knee flexion angles to best match theanatomy on the projected live images. Disadvantages of such techniquesare that large and expensive imaging apparatuses are required, and thatthey expose the patent to ionizing radiation. Moreover, these systemsare not suitable for use in most surgical settings due to their size andcomplexity.

In the article entitled ‘A system for ultrasound-guidedcomputer-assisted orthopaedic surgery’ by Chen et al, in Computer AidedSurgery, September/November 2005; 10(5/6): 281-292, a method fornon-invasive localizing a bone of a patient using two-dimensional (ieB-mode) ultrasound (US) is presented. Chen's method includes thefollowing points:

-   -   Preoperatively, a set of 2D freehand US images (e.g., a total of        2000 images) is acquired from the targeted anatomy along with        their corresponding positional information on the US probe.        These preoperative image data are used to construct a        preoperative database that serves two main purposes:        -   to construct a preoperative 3D volumetric representation of            the patient's anatomy that can be used for surgical planning            (stage no. 1 in FIG. 2),        -   to form a preoperative searchable image data-base for use by            the registration process.    -   Intraoperatively, the preoperative US volume is registered to        the patient using intraoperative 2D US images.        -   In the OR, the surgeon takes a few live US images of the            targeted anatomy while the position of the US probe is            tracked in real time by the camera system. These            intraoperative US images are used to find the physical            position of the patient during the surgery (see the lower            left image in FIG. 2).        -   A mutual information-based registration algorithm is            employed to find the closest match to the live image in the            preoperative image database (stage no. 2 in FIG. 2).        -   It should be borne in mind that the same images searched for            in the preoperative database are also the ones used to            construct the preoperative US volume of the targeted            anatomy. Assuming the closest matching image is actually the            live image, we can register the preoperative 3D US volume to            the live US image (the lower right image in FIG. 2) and thus            to the patient for surgical guidance (stage no. 3 in FIG.            2).

In other words, Chen's method involves constructing a large database ofa couple thousand localized 2D ultrasound images preoperatively, andcomparing each one of these images (or a reduced subset thereof) to anintra-operative localized ‘live’ 2D image of the bone. If there is agood match between one of the 2D images in the database and the live 2Dimage, it is assumed that the live image was acquired in the same planeas the localized one in the database. Therefore, a fundamentalrequirement of Chen's method to accurately track the bone is that theremust be a 2D image in the so-called preoperative database that has beenacquired in the same acquisition plane that the intra-operative US imagehas been acquired in, otherwise the matching algorithm cannot accuratelydetermine the location of the bone. Another drawback is that any patientmotion occurring during the pre-operative acquisition of 2000 or soimages will result in relative errors between the pre-op image slices inthe database (i.e. volumetric errors in the preoperative 3D US Volume).

SUMMARY

It is an object of the present invention to:

(1) Provide a non-invasive means for accurate and robust measurement andtracking of the motion of a bone using a volumetric US transducer;(2) Provide relative measurements of one bone relative to another boneof a joint;(3) Decompose relative joint motion into specific components; and(4) Measure joint kinematics, instability and range of motion.

In one embodiment, a method for non-invasively tracking a bone of asubject in three-dimensional space includes the following steps:

-   -   a. Acquiring a first reference image volume I0 of a bone surface        with a volumetric ultrasound imaging transducer at an initial        time to;    -   b. Acquiring a second image volume I1 of a bone surface with the        volumetric ultrasound imaging transducer at a second time t1;    -   c. Measuring the three-dimensional position of the volumetric        imaging transducer with a three-dimensional position measuring        device at times t0 and t1 and associating each position with the        corresponding image volumes I0 and I1;    -   d. Searching for a relative position of I0 and I1 for which the        overlapping portions of the image volumes of I0 and I1 best        match each other;    -   e. Determining the 3D transformation between the first reference        volume and the second image volume that corresponds to the        best-match position; and    -   f. Repeating steps b to e

BRIEF DESCRIPTION OF THE DRAWING FIGURES

FIG. 1 is a perspective view of a bone motion tracking system accordingto one embodiment of the present invention;

FIG. 2 a is an illustration of an ultrasound image volume A;

FIG. 2 b is an illustration of an ultrasound image volume B;

FIG. 2 c is an illustration of the ultrasound image volumes A and B in amatched position;

FIG. 3 is a schematic flow chart illustrating a tracking processaccording to the present invention; and

FIG. 4 is a perspective view of ultrasound image volumes on a femur.

DETAILED DESCRIPTION OF THE INVENTION

Referring now to FIG. 1, a computerized bone motion tracking system 1 isillustrated. The system is composed primarily of at least one of each ofthe following elements: a three dimensional (3D) positioning measurementsystem 20, a computer 10, a marking element 110, and a volumetricultrasound transducer 105.

Detecting and determining the position and orientation of an object isreferred to herein as “tracking” the object. The 3D positioningmeasurement system 20 is capable of detecting and determining theposition of marking elements 110 in a world coordinate system 40 (i.e.in 3D space). To provide precision tracking of objects, markers 10 canbe rigidly connected together to form reference bodies that have anassociated reference coordinate system 101, and these reference bodiesare attached to the ultrasound transducer 105, digitizing point probes120, tools, and other objects to be tracked. One such optical devicethat has been found to be suitable for performing the tracking functionis the Polaris™ system from Northern Digital Inc., Ontario, Canada. Theposition measurement device 20 is described in greater detail in anumber of publications, including U.S. Pat. Nos. 5,564,437 and6,725,082, both of which were previously incorporated by reference.

The 3D positioning measurement system 20, can be any type of systemknown in the art, including optical, infrared, electromagnetic,radiofrequency, ultrasound based, or any other type of positionmeasurement system. An example of a radiofrequency based tracking systemcan be found in United States Patent Application 2006/0250300, entitledRF system for tracking objects, which is hereby incorporated in itsentirety. Another example of a position measuring systems can be foundin United States Patent Application Publication number 2005/0245821,entitled Position Sensing System for Orthopedic Applications, which ishereby incorporated in its entirety.

The marking elements 110 are trackable by the 3D positioning measurementsystem 20. Thus the type of marking element corresponds to the type oftracking system employed, and can include passive retro-reflectivemarkers, active, infrared, magnetic (active or passive), radiofrequency,ultrasound based, etc.

The ultrasound transducer 105 is preferably a volumetric 3D or 4Dultrasound probe that is capable of acquiring a 3D image pixel volume104. In order to acquire 3D volumetric images the ultrasound transducer105 can contain a 2D surface array of transducing elements. Thisarrangement has the advantage that a 3D volume can be acquired virtuallyinstantaneously (i.e. in real time). In another embodiment, theultrasound transducer 105 contains a single row of elements that acquirea 2D planar image, and are translated or rotated by mechanical means inorder to build a 3D volume by acquiring a series of several image planeswhile registering the relative location of each plane. Volumetric 3Dultrasound probes are readily available today, such as those marketed bythe companies GE (General Electric Voluson™ 730 Pro) and Philips (Live3D Echo products, xMATRIX™http://www.medical.philips.com/main/products/ultrasound/products/technology/live_(—)3d.html#top).U.S. Patent Application Publication No. 20050033173 provides additionalbackground information on multi-dimensional 3D and 4D volumetricultrasound imaging devices. The volumetric ultrasound transducer 105 ispreferably a custom built transducer that has a linear or a concaveshape to better fit the patient and better image bone surfaces, whichare typically convex.

Marking elements 110 are rigidly attached to the ultrasound transducer105. Thus the position of the ultrasound transducer 105 and its imagingvolume 104 can be tracked in space, or in the co-ordinate system 40 ofthe positioning measurement system 20. The marking elements can beattached to ultrasound transducer 105 in one of many different positionsand can be locked in place before starting the bone-tracking step, forexample, to optimize visibility of the marking elements with respect tothe camera if an optical system is used. The marking elements could alsobe arranged so that they can be visible from any viewing angle, such asis described in U.S. Patent Application Publication No. 11/687,324,hereby incorporated by reference in its entirety. The ultrasoundtransducer 105 can be attached to the subject using any number ofdifferent means, for example, with straps 107, or adhesive tape or thelike. Alternatively, it could simply be held in place or pressed up tothe skin by an operator or by a mechanical arm that is attached to atable that the subject is lying on.

Marking elements 110 have an associated co-ordinate system 101 which isstored in the computer 30. Thus whenever the marking elements 110 arevisible and are being tracked by the positioning measurement system 20,the position of co-ordinate system 101 in the co-ordinate system 40 isknown at any instant in time. Image volume 104 has an associatedco-ordinate system 102. The relationship between co-ordinate system 101and 102 is fixed and can be known. The bone 2 has a co-ordinate system103 associated with it.

Referring now to FIG. 2 a, a close up view 300 of the ultrasound imagevolume 300 is shown, having a 3D image coordinate system 320. Imagecoordinate system 320 represents the coordinate system 102 in FIG. 1,and coordinate system 330 represents the marker coordinate system 101 inFIG. 1. A single 2D image slice 301 or cross section of the 3D imagevolume 300 is also shown schematically in FIG. 2. The image volume 300and slice 301 contains an image or representation 302 of the bonesurface 106, as well as any overlying bone tissues such as thepeilostium, muscles, ligaments, tendons, fascia and skin. The bonesurface 302 is at least partially visible in the image volume. Othertissues 305 overlying the bone surface can also be seen.

An overview of the steps of the tracking process are shown in FIG. 3. Atthe beginning of the bone tracking step 350, an initial reference imagevolume (I0) (image 300) of 3D ultrasound image data having co-ordinatesystem 320 is acquired and stored in the computer 30. For explanationpurposes, this reference image volume is acquired at time t0. Theposition of co-ordinate system 330 is also simultaneously acquired attime t0 (i.e., at the same time as the reference image volume 300) withthe position measurement system 20 and stored in the computer 30 asmatrix transformation TO. The transformation between the markercoordinate system 330 and the image coordinate system 320 is fixed asmentioned previously, since the markers are rigidly attached to theprobe 105. Using this initial reference volume 300 and transform T0, theinitial bone position is determined. At this point, an associated boneco-ordinate system 103 can be established that is linked to the markercoordinate system 330 and the image coordinate system 320 in the initialreference image volume dataset 350.

In step 355, a second image volume 400 (I1) (see FIG. 2 b) is acquiredwhile simultaneously tracking the ultrasound transducer 105 at time t1.This new image 400 can be another complete 3D image volume whoseposition is measured with the position measurement system 20 and storedin computer 30 as transformation matrix T1, and therefore known inspace. As can be seen in FIG. 2 b, the anatomical structures (302, 305)in the new image volume 400 may be displaced in the image coordinatesystem 420, in comparison to the reference image coordinate system 320due to underlying motion of the bone relative to the patients' skin andto the transducer 105.

As illustrated in FIG. 2 c, the new image 400 is then matched to theinitial reference image volume 300, in a 3D to 3D matching step 360. Inthe matching process, the new image 400 is displaced in the referenceimage coordinate system 320 and the overlapping areas of the two imagevolumes are compared to determine how well they correspond to each otherin each position. A mathematical optimization process is carried out tosearch for the relative position Tm that best aligns (or matches) thenew image with the reference image. Several techniques are known formatching image volumes to one another including intensity basedtechniques such as similarity measures, mutual information,correlations. The paper entitled Mutual Information-Based Rigid andNonrigid Registration of Ultrasound Volumes by R. Shekhar and V.Zagrodsky, published in IEEE Transactions on Medical Imaging 21, 1 Jan.2002, pp 9-22, teaches some methods of how to match or register two 3Dimage datasets with one another, and is hereby incorporated by referencein its entirety. Rigid or non-rigid matching may be performed. Manyvariations of the matching process are possible.

In a preferred embodiment of the present invention, only a select volumeor region of interest of image is used to match the two images. Limitingthe volume of pixels used in the matching process can increase the timetaken to find the best match, approaching near real-time trackingperformance. This region would ideally be the area 310 surrounding therigid bone surface 302. Using the region around the bone has theadvantage of avoiding inaccuracies due to poor matching because ofdeformations and relative movement of soft-tissues 305 such as muscles,vessels, fascia, and skin that are visible in image above the bonesurface. Tissue deformations can occur when the subject is moving orwalking, as in the case of gait analysis, or when the surgeon ismanipulating the joint of a patient undergoing surgery.

In another embodiment of the invention, the ultrasound transducer isplaced in an area in which soft tissues attach to the bone surface, suchas at the site of ligament, tendon or joint capsules insertions, etc,and are visible in the image 303. It is assumed that motion of thesetissues is negligible in the zone just above the bone surface. In thiscase, these tissues form an image texture 303 above the bone surface andare used to make the matching process more robust and accurate. Inaddition, if the bone surface was particularly symmetric or flat in theimage volume, the overlying texture 303 in the image can help thematching algorithm converge to the correct solution and can prevent thetwo images from sliding on the axis or in plane of symmetry andconverging to a false result. For example, if the bone shape in thereference and new images was primarily cylindrical, the matchingalgorithm could tend to converge at local minimum when the two cylindersare aligned but are not at the same axial position (due to thesymmetrical shape of the bone). The unique texture of the tissues justabove the bone surface could help to match the new image to thereference image in the correct axial location. The same advantages applyto planar and other symmetrical bone shapes.

The volume of interest 310 could be segmented out of the reference imagevolume just after the initial acquisition 350 and also in the new image355 just after it is acquired. Preferably fast, real-time, and fullyautomatic segmentation techniques are used. Several techniques forsegmentation of bone surfaces in ultrasound images have been publishedand are known. One example of a fully automated method for segmentingbone surfaces in ultrasound images can be found in the article A FullyAutomated Method for the Delineation of Osseous Interface in UltrasoundImages by V. Daanen, J Tonetti, J Troccaz, in C. Barillot, D. R. Haynor,and P. Hellier (Eds.): MICCAI 2004, LNCS 3216, pp. 549-557, 2004.Springer-Verlag Berlin Heidelberg 2004, which is hereby incorporated byreferences in its entirety. The region 310 can be defined for example byan offset from the bone surface, or by automatic analysis of the imagecontent and pattern around the surface.

Depending on the accuracy of the segmentation process, the matchingprocess can use either intensity (pixel) based or surface (geometrical)based techniques. Geometrical or surfaced based techniques have theadvantage of being very fast. Thus in one embodiment the bone surface inthe initial reference image volume 350 is segmented onto a discretesurface or set of points and matched with the same in the new image.Combinations of the two methods could also be used to take advantage ofthe features from both methods.

In another embodiment the new image acquired is not a complete 3D imagevolume but a sparse 3D volume that is reduced to a number of slices.These slices can be orthogonal to each-other (also known as 4D USimages), and the bone surface in each slice can be matched to the bonesurface in the initial reference image volume 350. This also has theadvantage of increased image transfer and matching speed.

Optionally, to increase the size of the initial reference image volume350, several additional located volumes of image datasets can beacquired adjacent to one another by moving the probe over the skinsurface in different directions while tracking the probe. Previouslyreferenced U.S. Patent Application 20050033173 entitled “Extended VolumeUltrasound Data Acquisition” provides details on one method that can beused for acquiring and constructing an extended image volume, which ishereby incorporated by reference in its entirety. This increases thetracking accuracy and robustness and allows more motion of theultrasound transducer relative to the bone during the tracking process.Preferably, the bone is moved as little as possible during this step.Overlapping images are acquired and are merged together to form oneenlarged ‘panoramic’ reference image volume. Information in theoverlapping areas can be used to match each image volume to one another,along with the position data acquired by the position measuring systemfor each scanned volume. As the bone may move slightly in space duringthe acquisitions however, the position data may not accurately representthe true relative positions of the bone surfaces imaged, and therefore,his data is best used only as an initial guess or estimate of therelative positions of the volumes. Rigid or non-rigid matching may beperformed with the actual image sets to more accurately construct theenlarged image reference image volume.

Once the new image has been matched to the reference image, the amountof motion (i.e. the change in displacement and orientation) thatoccurred between the bone and the ultrasound transducer from t0 to t1 isnow quantified by matrix transformation Tm. Thus the position of thebone can be tracked relative to the image coordinate system 102 of theultrasound transducer 105, whose position in 3D space is tracked by theposition measurement system 20. By tracking the position of theultrasound transducer 105 with marking elements 110 in the camerareference frame 40, we can track the bone in 3D space. Tools such aspoint probes 120, drilling and cutting guides, etc . . . can also betracked in space by attachment of marking elements 122. Thus theseobjects can be tracked relative to the bone by taking into account therelative motion of the ultrasound transducer 105 and tool 120.

To increase accuracy, more than one ultrasound transducer can be used totrack a bone. For example, transducers can be arranged at the hip 510and at the knee 520 so that the bone is localized at both ends. Thisway, small matching errors do not translate into large position errorsin areas relatively far from the image volume 104. Each ultrasoundtransducers can be connected together rigidly so that only one rigidbody needs to be tracked, or they can be localized individually to havegreater flexibility to move around. One transducer can be placed on themedial 530 and lateral 520 side of the bone as shown in FIG. 4. They canbe connected together using an adjustable arch that can adjusted andthen fixed to fit the different sizes and shapes of each patient.

The invention is particularly useful when tracking bones on either sideof a joint, such as the femur 2 and tibia 4 of the knee. Tracking of anybone or joint can be performed, including the hip (femur and pelvis) orshoulder (scapula and humerus) elbow, ankle, vertebrae, etc.

Particular zones on each bone can be identified that are easier toperform the imaging matching on (i.e., non-symmetrical bone surfaces andbone surfaces with tissue attachments). Such zones can include but arenot limited to the femoral greater trochanter, condylar areas, posteriorknee areas, tubercles such as the tibial tubercles, spine of thescapula, humoral greater trochanter, sacrum, anterior superior iliacspines, pubic tubrical, and so on.

EXAMPLE

The following paragraphs describe one example of how the presentinvention can be implemented.

The algorithm includes several steps and is outlined below. The firststep consists of producing a coarse segmentation of the bone interfacein the 3D ultrasound volume. The goal of the segmentation is to select aregion of interest in an area of the image which contains information. Aproperty of ultrasound images of bone is the presence of an acousticshadow under the bone surface interface, and as such there is noinformation in this region. In other words, it is not possible to imagestructures behind this interface. Then, from this coarse segmentation,synthetic images containing information of localization and distancefrom the bone interface are constructed. Finally, registration byintegrating the measure of similarity information provided by the rawimages and the synthetic images is performed. In the followingparagraphs, the different steps of our algorithm are set forth in moredetail.

Segmentation

The principle of the method for extracting points on the interface isbased on the physics of ultrasound waves. The physics of ultrasoundimaging indicates that the acoustic waves in a homogeneous mediumdecrease according to an exponential function. This property isexpressed as the following:

u(x)=u ₀exp^(−αx)

u(x)=u ₀exp^(−(alpha)x)

In the above equation, u₀ is the amplitude of the wave at the entrancein the medium, x represents the distance, and α (alpha) is theabsorption coefficient of the medium.

The idea for extracting the bone interfaces in the images is to try tocorrelate ultrasound profiles of ultrasonic beams with an exponentiallydecreasing function modeling the absorption of the acoustic wave in agiven medium. The correlation for local maxima of each ultrasoundscanline is calculated and when this correlation is higher than 90%, abone interface is considered to exist. To speed up the process, a lowerthreshold to remove local minima is applied, i.e., calculate thecorrelation for an intensity greater than or equal to 30. This thresholdis justified by the fact that the bone appears to be hyperechoic in theultrasound images.

The average absorption coefficient of ultrasonic waves in the (cortical)bone is on the order of 3 to 10 dB.cm⁻¹.MHz⁻¹. The bone stops ultrasonicwaves and they do not enter inside the bone so that we can calculate thecorrelations in the restricted depths (about 0.75 cm). This property ofthe bone explains the presence of the acoustic shadow behind the boneinterfaces.

For the 3D ultrasound volumes, the first step to extract the bonesurface is to apply the method described above on each scarline of theultrasound volume. The detection of the interface is not perfect becausethere is a lot of noise and ultrasound images can be of relative lowquality and there are outliers and “holes” in the surface. A few stepsare added therefore to “clean up” the surface. First, any isolated andsmall clusters of points are removed. The number of neighbor points(3×3×3 neighborhood) around the considered point are counted. Then, thepoint is kept only if the number of its neighbors is greater than orequal to (3×3−1)/2. We iterate until stability. To fill in the “holes”,a morphological dilatation is made by a sphere with a radius of 1 (toavoid the displacement of the interface while it is being thinned).Plane by plane is skeletonized to smooth and thin out the point cloud.Finally, a “bone morphing” step is performed in which a surface isdeformed to the cloud of points. At the end of the “bone morphing” step,we remove the outliers which are more than 1 mm from the surface areremoved. Finally, a second “bone morphing” step on the cleaned-up cloudof points is performed.

Panoramic Volume

Next, a panoramic ultrasound reference volume is built. Accurateregistration of 3D or 4D ultrasound images (images that may containlittle information) to a reference volume requires a maximum of overlap.It is thus advantageous to have a large reference volume.

The invention uses a 3D ultrasound/3D ultrasound voxel basedregistration method to match ultrasound volumes. The volumes can belocated in the world co-ordinate frame of the camera or with respect toa reference body attached non-invasively to the skin of the patient(i.e. an external marker attached to the patient non-invasively withstraps or adhesive tape). Because the patient may move during theacquisition or because the reference marker is not rigidly fixed to thestructure to track, it is necessary to compensate for this movementduring the acquisitions of the panoramic volume. This method ofregistration allows one to build panoramic volumes to compensate for thesmall size of the original volumes and maximize the overlap between the4D images and the reference volume for the dynamic tracking (i.e. thenext step)

The particularity of the present registration method is to combine theinformation given by the intensities contained in the image and theinformation given by a coarse segmentation of our images.

The first stage of the registration algorithm is to produce a coarsesegmentation of the bone interface using the method that was explainedpreviously. This segmentation can define different regions in the image:regions corresponding to the bone interface, regions ahead of interface,regions behind the interface and regions with no specific information.Starting from the distinction between these different regions, a conceptof distance to the interface has been added which enables the buildingof an image containing this information. This image is constructed asfollows: the bone interface (obtained by the segmentation) is modelizedby a Gaussian, for the regions located in front of and behind theinterface a linear model is used. This linear model represents thedistance to the interface. The others regions are not considered.

To register the images, a voxel-based registration method is used. Thenormalized cross-correlation is used. The optimization procedure is thePowell-Brent algorithm. The similarity measure is modified to integratethe information containing in the synthetic images. A multiplicativefactor (pixel to pixel) is calculated which penalizes the similaritymeasure calculated on the raw image. This factor is a kind of normalizedSSD (sum of the square differences) calculated pixel-to-pixel on theimages.

Bone Tracking

The bone tracking step requires a <<real time>>3D/3D or 3D/4D ultrasoundregistration algorithm (i.e. to constantly register new images to thereference volume). The 3D/3D registration algorithm described previouslyfor building a panoramic volume can be naturally extended for tracking.This algorithm can be optimized to match (or register) the bone in orderto track it in real-time, using a multi-resolution approach, and/or byperforming calculations on a graphics board (video card) to speed up theprocess and computation time. As mentioned previously, the algorithm canregister either a 3D volume obtained in “real time” (for example, with amatrix probe) or two orthogonal ultrasound slices obtained in “realtime” (for example, with a mechanical probe) to the reference volume.The initial attitude (i.e. the transformation used as the initial‘guess’ of the best-match search algorithm) used for the registration atthe instant t_(i+1) can be given by the previous registration at theinstant t_(i) and should be close to the best ‘matched’ solution.Consequently, the size of the research space is reduced and thus theregistration process is faster.

In one embodiment of the present invention, the non-invasive bonetracking system is used to measure relative motion of at least two bonesof a joint, in which one bone is tracked with the non-invasiveultrasonic method, and the other bone is tracked by simply attaching themarking elements 112 to the skin with straps 112 or plates. A cast couldalso be used to fix the second tracker to the patient, such as on thetibia or arm. To measure shoulder motion and stability, a cast can beput around the for-arm and biceps to fix the elbow at a particularflexion angle, such as at 90 degrees. Scapular motion can then bemeasured by strapping the tracked ultrasound transducer to the spine ofthe scapula or near the neck of the gleniod on the posterior side.

Some examples of use of the system are as follows: knee stabilitytesting to diagnose an injury or to compare pre and post operativekinematics. Tests such as the Anterior posterior drawer test, lauchmantest, pivot shift test, varus valgus stress test could be quantifiednon-invasively. U.S. Patent Application Publication No. 20060161052entitled “Computer assisted orthopaedic surgery system for ligamentgraft reconstruction describes methods for calculating theabovementioned parameters, and for decomposing relative joint motioninto specific components”, which is hereby incorporated by reference inits entirety. Hip range of motion could also measured pre andpost-operatively, and gait analysis can be performed eliminating theerrors due to skin motion. Shoulder range of motion, stability, scapularkinematics can be quantified. The system is also adapted for surgicaluse such as orthopaedic procedures.

It will be appreciated by persons skilled in the art that the presentinvention is not limited to the embodiments described thus far withreference to the accompanying drawings; rather the present invention islimited only by the following claims.

1. A method for non-invasively tracking a bone of a subject inthree-dimensional space, the method comprising: (a) acquiring a firstreference image volume I0 of a bone surface with a volumetric ultrasoundimaging transducer at an initial time to; (b) acquiring a second imagevolume I1 of a bone surface with the volumetric ultrasound imagingtransducer at a second time t1; (c) measuring the three-dimensionalposition of the volumetric imaging transducer with a three-dimensionalposition measuring device at times t0 and t1 and associating eachposition with the corresponding image volumes I0 and I1; (d) searchingfor a relative position of I0 and I1 for which overlapping portions ofthe image volumes of I0 and I1 are closest aligned to one another anddefining this position as a best-match position; (e) determining the 3Dtransformation between the first reference volume and the second imagevolume that corresponds to the best-match position; and (f) repeatingsteps b to e.
 2. The method of claim 1, wherein the best-match search islimited to a smaller region of interest that includes the pixelsrepresenting the bone surface in at least one of the reference imagevolume and the second image volume.
 3. The method of claim 1, whereinthe second image volume is a sparse 3D volume.
 4. The method of claim 3,wherein the sparse 3D volume is limited to two to three orthogonal imageplanes.
 5. The method of claim 2, wherein the region of interestincludes the bone surface and a finite region of soft-tissues overlyingthe bone surface.
 6. The method of claim 1, wherein the determined 3Dtransformation is used as an initial guess for the first relativeposition used in the best match search of step d for the next successivetracking step.
 7. The method of claim 1, wherein the first referencevolume is an extended panoramic volume made up of several image volumesacquired adjacent to one another and matched with one another.
 8. Themethod of claim 1, wherein the bone to be tracked is one of a femur,tibia, scapula, humerus, pelvis, scaphoid or vertebra.
 9. The method ofclaim 1, wherein the bone to be tracked is the femur bone of a kneejoint, and a second marking element is non-invasively attached to thetibia.
 10. The method of claim 1, wherein the bone to be tracked is ascapula bone of a shoulder joint, and a second marking element isnon-invasively attached to the humerus
 11. The method of claim 10,wherein the relative motions of the bones of the joint are measured anddecomposed in to different directions and axes of rotation.
 12. Themethod of claim 1, wherein multiple volumetric transducers arepositioned at different locations to track a bone.
 13. The method ofclaim 12, wherein the multiple volumetric transducers are rigidlyconnected to one another and tracked by a marking element.
 14. Themethod of claim 1, further including the step of displaying the trackedbone on a display and showing movement thereof in approximatelyreal-time.